Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps

Article

关键词: SCHRODINGER-OPERATORS;    EIGENVALUE BOUNDS;    SPECTRAL GAPS;    GUIDED MODES;    PROOF;    STATE;   

DOI  :  10.1103/PhysRevB.81.155324

来源: SCIE

【 摘 要 】

We prove, via an elementary variational method, one-dimensional (1D) and two-dimensional (2D) localization within the band gaps of a periodic Schrodinger operator for any mostly negative or mostly positive defect potential, V, whose depth is not too great compared to the size of the gap. In a similar way, we also prove sufficient conditions for 1D and 2D localization below the ground state of such an operator. Furthermore, we extend our results to 1D and 2D localization in d dimensions; for example, by a linear or planar defect in a three-dimensional crystal. For the case of D-fold degenerate band edges, we also give sufficient conditions for localization of up to D states.

【 授权许可】

Free